Final Answer
$3x^{2}+7x-6$
Step-by-step explanation
Problem to solve:
$\frac{12x^3+13x^2-59x+30}{4x-5}$
1
Divide $12x^3+13x^2-59x+30$ by $4x-5$
$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}-5;}{\phantom{;}3x^{2}+7x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}-5\overline{\smash{)}\phantom{;}12x^{3}+13x^{2}-59x\phantom{;}+30\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}-5;}\underline{-12x^{3}+15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-12x^{3}+15x^{2};}\phantom{;}28x^{2}-59x\phantom{;}+30\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-5-;x^n;}\underline{-28x^{2}+35x\phantom{;}\phantom{-;x^n}}\\\phantom{;-28x^{2}+35x\phantom{;}-;x^n;}-24x\phantom{;}+30\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-5-;x^n-;x^n;}\underline{\phantom{;}24x\phantom{;}-30\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}24x\phantom{;}-30\phantom{;}\phantom{;}-;x^n-;x^n;}\\\end{array}$
2
Resulting polynomial
$3x^{2}+7x-6$
Final Answer
$3x^{2}+7x-6$